James S. Pappas (1922-2007) spent most of his active mathematical career at White Sands Missile Range (WSMR) in southern New Mexico. He first appeared at WSMR in 1952 after receiving a bachelor’s degree in Mathematics and a master’s degree in Physics. What was then called the White Sands Proving Ground offered him the opportunity to work in applied mathematics as the USA was moving into more advanced missile systems and the test range into the use of multidimensional matrix methods. As can be seen from his writings, advanced missile guidance and multi-radar tracking systems were the backbone of his early work.

Upon arriving at WSMR, he was assigned to work under the direction of Guenther Hintze, one of only three of the original Wernher von Braun V-2 German scientists who stayed at the range when in 1949 the rest moved to Redstone Arsenal in Alabama. Guenther, whose signature is found on several of Pappas’ early reports, headed up the Analysis and Computation Directorate at the range.

As can be seen by the various publications, Pappas started at White Sands documenting the state of the art of missile guidance and control. His knowledge of vehicle guidance actually began in Fort Worth at Convair Aircraft where he worked for a couple years. The work at WSMR quickly moved to multi-base least squares methods and Kalman filtering (1967). Pappas brought Dr. Kalman to WSMR to present a set of lectures and they developed a friendship (see letter). The bulk of his writings cover Kalman filtering and matrix methods. As US defense spending changed in the early 1970’s so did WSMR. The excitement of space race spending of the 60’s and 70’s came to a close, so did the DOD’s desire to spend money on basic science. WSMR reached a peak of missile testing in 1969 with 3,814 missile tests, but by 1977 that number was reduced to 1,170, the lowest since 1954. The Department of Defense was seeking a big shift in the way it does basic research. The glory days of the range was coming to an end. By the end of the 1970’s there was no need for Pappas’ services, so he retired. His last work was a two volume set on Kalman filtering and recursive optimal estimating in 1977.

Pappas does not seem to bring any particular unique contribution to the mathematical field, but his love for Gibbsion vectors and Dirac notation is notable. He does claim the following: “Optimization, using the gradient of the trace of products of matrix valued functions, including the generalized inverse, are presented in a novel state-space setting. A number of functions of such products of matrices, including general formulas, are derived for the first time to our knowledge.” (“New Gradient Techniques for Traces of Function of Rectangular Matrices and their Pseudo-Inverses”, 1977).

His work demonstrates a solid command and understanding of applied vectors as he expresses with ease and simplicity all aspects of abstract algebra as applied to vectors. He moves the complex to a simplistic elegance as he sees the beauty and full potential of this type of vector representation. It is like watching the finest of artist expand his talent, creating and expanding on what some call the bra-ket notation to include a clean precise applied vector notation. One can see the applied nature of the vector space analysis by his ability to keep track of the size of the n-tuples using his unique modified Dirac notation.

Publications:

Dr. Kalman's letter to Pappas.

Mathematical Modeling for Missile Systems., James S. Pappas, Mar 1959.

General Considerations for Satellite Attitude Control Systems., White, John S. ; Pappas, James S, 25 JAN 1961.

MATRIX METHODS APPLIED TO THE GIBBSION VECTORS AND DYADICS WITH APPLICATIONS TO FLIGHT DYNAMICS., PAPPAS,JAMES S., OCT 1962.

Derivation of the Euler Angle Rate Equations Using Rotation Axes as a Non-Orthogonal Bases, With Tables of Matrix Equations for the Rotation Sequences., James S. Pappas, May 1963.

TECHNIQUES FOR MAPPING NON-LINEAR VECTOR-DYADIC FLIGHT SYSTEM EQUATIONS TO STATE-VECTOR FORM FOR COMPUTER MECHANIZATION., Pappas,James S. ; Carrillo,Jesus E., 03 OCT 1963 (No document).

A STATE VECTOR DERIVATION OF A DETERMINISTIC SIMULATION MODEL OF A RADAR TRACKER ON A ROTATING EARTH, PAPPAS,James S. ; McDaniel,Robert E., APR 1963 (No document).

MATH MODEL OF GRAVITY TORQUES AND INTERNAL TORQUES CAUSED BY GYROS AND INERTIA WHEELS ON AN EARTH-POINTING ORBITING VEHICLE., Pappas,James S., FEB 1964 (No document).

APPLICATION OF THE KALMAN FILTER TO SEQUENTIAL OPTIMAL PARAMETER ESTIMATION VIA HOUSEHOLDER'S MATRIX INVERSION METHOD., Pappas S. James, JUN 1967.

A MATH MODEL FOR COMPUTING NOISE VARIANCE MATRICES FOR A SYSTEM OF RADAR TRACKERS., Pappas,James S. ; Diaz,Alfonso., JUL 1967 (No document).

A VECTOR SPACE DERIVATION-USING DYADS-OF WEIGHTED LEAST SQUARES FOR CORRELATED NOISE., Pappas, James S., JUN 1968.

A TUTORIAL DERIVATION OF RECRUSIVE WEIGHTED LEAST SQUARES STATE-VECTOR ESTIMATION THEORY (KALMAN THEORY), Pappas, James S., AUG 1968.

State Space Techniques for Inertial Measurement Unit Variables for Range Tests., Pappas,James S. ; Orlov,Robert D., APR 1972 (No document).

TRANSFORLMATIONS FOR RANGE INSTRUMENT COORDINATES AND THEIR TRACKING SPACE SINGULARITY REGIONS., James S. Pappas., Glenn A. Bookhout , June 1972 (No document).

Applications of Optimization Theory to Data Processing at WSMR., James S. Pappas, May 1974 (No document).

New Derivations and Matrix Comparisons of the Bodwell and Odle Position Vector Solutions from Sight Line Measurements., James S. Pappas, Aug 1974.

New Gradient Techniques for Traces of Functions of Rectangular Matrices and Their Pseudo-Inverses, Pappas,James S. ; Dalton,Oren N., SEP 1977.

State Space Techniques in Approximation Theory with Applications to Design of Recursive Optimal Estimators. Volume I., Pappas,James S., SEP 1977.

State Space Techniques in Approximation Theory with Applications to Design of Recursive Optical Estimators. Volume II., Pappas.,James S., SEP 1977.